Thermoelectric materials convert a temperature gradient into electricity and vice versa.
They are of considerable current interest for solid state power generation from heat and refrigeration from electricity without moving parts. While all semiconducting materials have a non-zero thermoelectric effect, in most materials it is too small to be useful.
The thermoelectric figure of merit
  ZT  =                              S          2                ⁢        σ            κ        ⁢    T  measures the thermoelectric efficiency of a material, where S is the Seebeck coefficient reflecting the thermoelectric power of the material, σ is the material's electrical conductivity, κ is its thermal conductivity, and T is the absolute temperature. These parameters depend on both the electronic and the phonon transport properties of the material, with the ideal thermoelectric material having high S, high σ, and low κ.
The enormous potential of high-efficiency thermoelectric devices has led to decades of work aimed at optimizing these parameters in semiconductor and semimetal compounds in an attempt to increase ZT.
Unfortunately, the parameters of ZT are interdependent, such that changing one alters the others. As a result, it is often found that the resulting changes in ZT are minimal. See A. Majumdar, “Thermoelectricity in Semiconductor Nanostructures,” Science 2004, 303, 777-778.
For example, the Seebeck coefficient S is a fundamental material property related to carrier effective mass and is typically difficult to engineer. In general, single-carrier materials (e.g. n- or p-type doped semiconductors) can achieve S in a suitable magnitude. In addition, in semiconductors, electrical conductivity σ can be increased by increasing the doping level. Thus, highly doped semiconductors can often satisfy the first two requirements for obtaining a high ZT, i.e., having a large Seebeck coefficient and high electrical conductivity. However, too much doping will drive a semiconductor into a metallic state and so will eventually reduce S. Therefore, obtaining a proper doping level that will achieve a high S2σ is difficult.
The plots in FIG. 1, which are modified from those shown in G. J. Snyder et al., “Complex thermoelectric materials,” Nature Materials 7, 105-114 (2008), illustrates this dilemma. As can be seen from FIG. 1, as carrier concentration increases, the Seebeck coefficient S decreases while the electrical conductivity σ increases. S2σ also increases as carrier concentration increases, but only up to a certain level in carrier concentration, after which the decrease in S so outweighs the increase in conductivity σ that the combined value of S2σ also decreases.
In addition, increasing electrical conductivity σ in semiconductors will inevitably increase the thermal conductivity κ because the charge carriers that conduct electricity also conduct heat in addition to phonons, and most known mechanisms that would reduce phonon transport will hinder charge carrier transport as well.
The scientific community has focused its efforts on finding ways to reduce κ that have minimal effects on charge carrier transport. For example, one common way to reduce heat conduction is to introduce phonon scattering centers for phonons responsible for heat conduction.
The problem is that heat is carried by a broad band of phonons having wavelengths ranging from less than 1 nm to over 1000 nm. Since the phonon scattering centers have to be effective for the whole phonon bandwidth, the scattering centers that reduce thermal conductivity will almost inevitably also scatter charge carriers, thereby reducing electrical conductivity as well. The conventional approach to reduce phonon transport is to use grain boundaries to scatter phonons. Phonons are most effectively scattered by crystalline grains having the same size as the phonon wavelength, analogous to Rayleigh scattering of photons. In order for more substantial phonon scattering the entire phonon spectrum must be addressed with a matched distribution of grain sizes.
In the past two decades, there has been significant activity in thermoelectric research.
Approaches that have been used to reduce κ have included use of PbSeTe-based quantum dot superlattice structures, see T. C. Harman et al., “Quantum Dot Superlattice Thermoelectric Materials and devices,” Science 297, 2229 (2002); and embedding ErAs nanocrystallites in crystalline InGaAs thin films, see W. Kim et al. “Reducing Thermal Conductivity of Crystalline Solids at High Temperature Using Embedded Nanostructures,” Nano Lett. 8, 2097 (2008).
Some of the other approaches used to reduce κ include alloying (e.g. alloying Si with Ge to obtain Si80Ge20), use of heavy elements (Bi2Te3), and using materials having “rattling” modes in their crystal structures (CoSb3). See, e.g., S. K. Bux et al., “Nanostructured Bulk Silicon as an Effective Thermoelectric Material,” Adv. Funct. Mater. 2009, 19, 2445-2452; W. Liu et al., “Recent advances in thermoelectric nanocomposites,” Nano Energy (2012) 1, 42-56; and D. J. Voneshen et al., “Suppression of thermal conductivity by rattling modes in thermoelectric sodium cobaltate,” NATURE MATERIALS, Vol. 12 (November 2013), pp. 1028-1032.
Dependence of thermal conductivity on nanocrystalline size in BiTe-based thin film systems and bulk silicon germanium alloys has also been reported. See M. Takashiri et al., “Effect of grain size on thermoelectric properties of n-type nanocrystalline bismuth-telluride based thin films,” J. Appl. Phys. 104, 084302 (2008) (“Takashiri 2008”). see also X. W. Wang et al., “Enhanced thermoelectric figure of merit in nanostructured n-type silicon germanium bulk alloy,” Appl. Phys. Lett. 93, 193121 (2008); G. Joshi et al., “Enhanced Thermoelectric Figure-of-Merit in Nanostructured p-type Silicon Germanium Bulk Alloys,” Nano Letters 2008, Vol. 8, No. 12, 4670-4674.
One newly explored approach has been to use nanostructured materials as thermoelectrics, motivated by early theoretical work which predicted the benefits of nanostructuring for increasing ZT. See, e.g., L. D. Hicks et al., “Effect of quantum-well structures on the thermoelectric figure of merit,” Phys. Rev. B 47, 12727-12731, 1993; and L. D. Hicks et al., “Thermoelectric figure of merit of a one-dimensional conductor,” Phys. Rev. B 47, 16631-16634 (1993).
Incorporation of nanostructures in addition to the legacy approaches described above has allowed for materials that reduce κ with minimal effect on G, resulting in drastic improvements in ZT. Recently, ZT of ball-milled nanocrystalline SiGe alloys has reached 1.84. See R. Basu et al., “Improved thermoelectric performance of hot pressed nanostructured n-type SiGe bulk alloys,” J. Mater. Chem. A, 2014, 2, 6922-6930. In thin film systems, thermal conductivity has been reduced significantly by the use of interfaces in a Bi2Te3/Sb2Te3 superlattice, reaching a maximum of ZT=2.4. See R. Venkatasubramanian et al., “Thin-film thermoelectric devices with high room-temperature figures of merit,” Nature 413, 597 (2001). In bulk material, a maximum ZT=2.2 has been achieved in a PbTe bulk material with nanoparticulates of SrTe and an extremely high Na (p-type) doping concentration. See K. Biswas et al., “High-performance bulk thermoelectrics with all-scale hierarchical architectures,” Nature 489, 414-418 (2012).
These results demonstrate the power of nanostructures in reducing κ and decoupling electrical and thermal conductivities, but do not offer a route for practical manufacturing, and suitable nanostructured materials are often expensive and difficult to prepare.
Nanocrystalline thermoelectric materials have previously been made using a ball-milling process whereby doped crystalline silicon is ground together with a few atomic percent of germanium to produce nanometer-sized fine grains which are subsequently hot-compressed into bulk material. Recently, ball-milling has been used to successfully fabricate bulk thermoelectric materials having a ZT reaching 1.84. See Basu et al., supra; Joshi et al., supra, and Wang et al., supra; see also U.S. Pat. No. 7,255,846 to Ren et al., “Methods for synthesis of semiconductor nanocrystals and thermoelectric compositions”; U.S. Pat. No. 7,465,871 to Chen et al., “Nanocomposites with high foreign patent documents thermoelectric figures of merit”; U.S. Pat. No. 8,512,667 to Yang et al., “High Temperature Stable Nanocrystalline SiGe Thermoelectric Material”; and U.S. Patent Application Publication No. 2008/0202575 to Ren et al., “Methods for high figure-of-merit in nanostructured thermoelectric materials.”
Ball-milling is less expensive than the more complicated techniques such as use of superlattices and quantum dots. However, the smallest grain size that ball-milling can obtain is about 10 nm, which is not small enough to scatter phonons having wavelengths smaller than that size, while at room temperature and above the majority of phonons have wavelengths smaller than 10 nm. To solve this problem, Ge is often added to the nanocrystalline structure to generate impurity scattering centers for short wavelength phonons.
Chemical vapor deposition (CVD) generates thin film nc-Si thermoelectric materials directly on a substrate as opposed to producing a nanopowder which must then be formed into a solid as does ball-milling. Thin film CVD-based deposition techniques have not been widely used to fabricate thermoelectric materials, although some preliminary research in this direction has been reported, see M. Takashiri et al., “Transport properties of polycrystalline Si0.8Ge0.2 thin films for micro power generators,” Proceedings ICT'03. 22nd International Conference on Thermoelectrics (IEEE Cat. No. 03TH8726), Pages: 395-8 (2003) (“Takashiri 2003”), and recently, CVD techniques have been used to harvest nanocrystalline SiGe powder which is then compressed to make bulk thermoelectric material. See Takashiri 2003, supra; see also T. Claudio et al. “Nanocrystalline silicon: lattice dynamics and enhanced thermoelectric properties,” Phys. Chem. Chem. Phys. 2014, 16, 25701-25709. However, the nanocrystalline silicon produced by the Takashiri group had grain sizes of at least 20 nm, while the nanocrystalline silicon produced by the Claudio group had even larger grain sizes over 30 nm. The large grain size of these previous CVD-prepared materials limits the improvement of ZT and makes the technique not as competitive as the ball-milling technique.
In addition, these prior art films all require the use of a silicon-germanium alloy, where Ge is used to scatter short-wavelength phonons and thereby reduce the thermal conductivity of the material. See, e.g., M. Takashiri et al., “Structure and thermoelectric properties of boron doped nanocrystalline Si0.8Ge0.2 thin film,” J. Appl. Phys. 100, 054315 (2006) (“Takashiri 2006”).
However, mixing Ge with Si has a number of problems. Ge is expensive, 1000 times more expensive than Si, making the use of such SiGe alloys impractical in many cases. Ge has a higher electron affinity than does Si, so that the addition of Ge impedes the transport of electrons through the material, reducing its electrical conductivity. Finally, Ge has a lower melting point than does Si, limiting the temperature range at which a SiGe alloy can be used.